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Discrete Math and Analyzing Social Graphs
Week 2
Numbers with Non-increasing Digits

Practice QuizPractice Quiz • 10 min10 minutes

Numbers with Non-increasing Digits

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Numbers with Non-increasing Digits

Practice Quiz • 10 min

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Numbers with Non-increasing Digits

Total points 1

1.

Question 1

Note that this is a practice quiz. This problem will be discussed in the next video, but we encourage you to try to solve it yourselves first.

How many four-digit numbers are there such that their digits are non-increasing, that is each next digit is not greater than the previous one? Three-digit numbers are also four-digit, they just start with 0.

1 / 1 point

715

Correct

This is correct! To fix such a number it is sufficient and enough to pick unordered subset of four numbers from 0 to 9. Then they can be ordered into a non-increasing order in a unique way. Since there might be equal digits in our number, repetitions are allowed. Thus we are dealing with combinations of size 4 out of 10 options with repetitions.

See the next video for discussion.